Simplify by removing factors of 1 . \( \frac{36 q^{8}}{45 q^{11}} \) \( \frac{36 q^{8}}{45 q^{11}}=\square \) \( ( \) Simplify your answer.)

To simplify \( \frac{36 q^{8}}{45 q^{11}} \), we can start by reducing the numerical coefficients. The greatest common divisor (GCD) of 36 and 45 is 9. Dividing both the numerator and denominator by 9 gives us: \[ \frac{36 \div 9}{45 \div 9} = \frac{4}{5} \] Next, we look at the variable part \( q^{8} \) and \( q^{11} \). Since the denominator has a higher exponent, we subtract the exponents: \[ q^{8-11} = q^{-3} \] Putting it all together, we get: \[ \frac{4}{5} q^{-3} \] To express it with positive exponents, we write: \[ \frac{4}{5 q^{3}} \] So finally, \[ \frac{36 q^{8}}{45 q^{11}} = \frac{4}{5 q^{3}} \]